The woman who has accused Brett M. Kavanaugh of sexual assault decades ago wants the FBI to investigate her allegation before she testifies before the Senate Judiciary Committee — a demand that came as President Trump and Senate Republicans increasingly rallied to the defense of the embattled Supreme Court nominee.

“A full investigation by law enforcement officials will ensure that the crucial facts and witnesses in this matter are assessed in a non-partisan manner, and that the committee is fully informed before conducting any hearing or making any decisions,” lawyers for the woman, Christine Blasey Ford, said in a letter to the panel late Tuesday.

The committee had invited Kavanaugh and Ford to testify at a public hearing Monday, but Ford’s response raises questions about whether the GOP will proceed with the session and ultimately the vote on Kavanaugh, who was nominated in July to replace the retired Justice Anthony M. Kennedy. The two-page letter does not explicitly say she will not attend if there is no FBI probe.

Many Republican officials maintained Tuesday that such a hearing would be Kavanaugh’s best chance at preserving his nomination to the high court, since it would give the judge — who seems determined to fight the allegation — an opportunity to respond to the claims. But Democrats, like Ford, argued that the scheduled Monday session should be delayed until the FBI further investigates her allegation.

The letter from Ford’s lawyers described death threats and harassment since The Washington Post published her account Sunday.

“In the 36 hours since her name became public, Dr. Ford has received a stunning amount of support from her community and from fellow citizens across our country. At the same time, however, her worst fears have materialized,” the letter said. “She has been the target of vicious harassment and even death threats. As a result of these kind of threats, her family was forced to relocate out of their home. Her email has been hacked, and she has been impersonated online.”

The letter also refers to Ford testifying “at the same table” as Kavanaugh, although a spokesman for Senate Judiciary Committee Chairman Charles E. Grassley (R-Iowa) said it was never the plan, nor was it conveyed to Ford and her attorneys, to have them testify together.

In a statement late Tuesday night, Grassley disputed that the FBI would need to investigate before Ford appeared before the committee and said: “The invitation for Monday still stands.”

“Dr. Ford’s testimony would reflect her personal knowledge and memory of events,” Grassley said. “Nothing the FBI or any other investigator does would have any bearing on what Dr. Ford tells the committee, so there is no reason for any further delay.”

The FBI declined to comment Tuesday after the letter from Ford’s lawyers was made public. The Justice Department said previously that the FBI updated Kavanaugh’s background-check file to include the allegation and suggested that that is the extent of what the agency plans to do.

Sen. Dianne Feinstein (Calif.), the top Democrat on the Judiciary Committee, urged Republicans to delay Monday’s hearing after Ford’s lawyers sent their response. The high-stakes hearing was set without consultation with Ford, although Grassley’s office has said his staff offered Ford multiple dates for a potential hearing.

“I agree with her 100 percent that the rushed process to hold a hearing on Monday has been unfair and is reminiscent of the treatment of Anita Hill,” Feinstein said, referring to the woman who testified in 1991 that now-Justice Clarence Thomas had sexually harassed her. “I also agree that we need the facts before senators — not staff or lawyers — speak to witnesses.”

Earlier, Democrats protested Republicans’ decision to limit the witnesses at Monday’s hearing to just Ford and Kavanaugh, saying it would turn the testimony into a “he said, she said” spectacle.

At a White House news conference Tuesday afternoon, Trump encouraged the hearing to proceed so Ford can “state her case,” but he predicted that the public setting would ultimately exonerate Kavanaugh and expressed sympathy for his nominee.

“I feel so badly for him that he’s going through this,” Trump said. “. . . This is not a man that deserves this.”

He called Kavanaugh “a great gentleman” and lamented that his wife and daughters are experiencing the public airing of accusations that Trump said Feinstein should have brought up earlier in his confirmation process. Feinstein has said she kept the accusation confidential at Ford’s request.

Though Kavanaugh’s confirmation prospects looked shaky earlier this week after Ford’s allegations became public, senior Republicans on Tuesday were increasingly determined to press forward with his nomination.

“All I can say is that we’re bringing this to a close,” said Sen. Lindsey O. Graham (R-S.C.). “They’ve had tons of time to do this. This has been a drive-by shooting when it comes to Kavanaugh. . . . I’ll listen to the lady, but we’re going to bring this to a close.”

Sen. Rob Portman (R-Ohio), a close Kavanaugh friend who introduced him at his confirmation hearings this month, said, “Obviously, the process was very unfair.” He added: “I’m not blaming [Ford], I’m blaming the Democrats who misused this process.”

And Sen. John Cornyn (Tex.), the No. 2 Republican in the Senate, sharply questioned Ford’s credibility. Speaking to reporters, Cornyn said he was concerned by “gaps” in the account of Ford, who told The Washington Post that, at a house party in the early 1980s when the two were in high school, Kavanaugh drunkenly pinned her to a bed, groped her and put his hand over her mouth to stifle her screams.

“The problem is, Dr. Ford can’t remember when it was, where it was or how it came to be,” Cornyn told reporters at the Capitol.

Asked whether he was questioning the accuser’s account, Cornyn said, “There are some gaps there that need to be filled.”

In another part of the dispute, Democrats insisted that Mark Judge, a Kavanaugh friend from their time at Georgetown Preparatory School, should appear before the panel to testify about the alleged incident.

Republicans “have just completely tried to ram this thing through,” said Sen. Patrick J. Leahy (D-Vt.), a former chairman of the committee. “This is more of the same.”

Judge, who Ford said was in the room at the time of the alleged assault, said in a letter to the committee that he did not wish to speak publicly. In the letter, relayed by his attorney, Judge said that he has “no memory of this alleged incident.”

“Brett Kavanaugh and I were friends in high school, but I do not recall the party described in Dr. Ford’s letter,” Judge said. “More to the point, I never saw Brett act in the manner Dr. Ford describes.”

GOP staffers on the Judiciary Committee continued reaching out to other potential witnesses mentioned in The Post’s report Sunday, as Kavanaugh visited the White House for the second day in a row Tuesday. Trump said he had not spoken to him.

The coordination and preparation for Monday’s hearing has largely been centered on the White House. Kavanaugh and White House counsel Donald McGahn, along with other White House officials, met Monday and Tuesday for hours, monitoring news coverage and talking through their strategy, as Kavanaugh personally called senators to press his case.

White House officials engaged in a two-hour practice session, known as a murder board, in the Eisenhower Executive Office Building with Kavanaugh, where he answered questions on his past, his partying, his dating and the accuser’s account. Participants included McGahn, deputy chief of staff Bill Shine, press secretary Sarah Huckabee Sanders and Raj Shah, who is leading communications.

It was unclear whether Monday’s hearing would take place if Ford formally turns down the committee’s invitation. Cornyn said that if Ford “doesn’t want to participate, then we can’t force her.” A committee vote on Kavanaugh, initially scheduled for Thursday but subsequently canceled, could occur “a couple days” after that hearing, Cornyn said.

The charged political dynamics ahead of November’s midterm elections hovered as some Democrats running for reelection in states won by Trump in 2016 shied away from reporters, as did some moderate Republicans worried about potentially alienating independent voters and women.

Sen. Patty Murray (D-Wash.) was first elected in the 1992 “year of the woman” following the 1991 hearings for Thomas. She said Republicans risk another Democratic surge if they aggressively target Kavanaugh’s accuser.

“They’re on very fragile ground,” Murray said. “If women and men believe someone who has courageously come forward isn’t being treated fairly, there will be a reaction, you can count on that.”

More than 140 female friends of Ford signed a letter Tuesday defending the Palo Alto University professor and her character. “Christine’s bravery and sacrifice in coming forward with her story while knowing the all-but-certain to follow devastating consequences for and retaliation against her and family does not surprise those of us who know her,” the letter read. “We are all very proud of Christine, grateful to have her as a member of our community, and stand in solidarity with her.”

While many Republicans remain confident that Kavanaugh will be confirmed, there have been private discussions among some lawmakers about whether the GOP should have a backup plan if he withdraws from the process or fails to secure the necessary votes.

But any private skepticism was outweighed by public vows to stand by Kavanaugh as he fought the allegation.

“He’s not going to withdraw,” Cornyn insisted. “I talked to him yesterday, and he’s determined to testify and tell his side of the story.”